- #1
DudleySquires
- 4
- 0
Hello folks. After a while lurking I've finally got a problem that I need some help with!
1. Homework Statement
I'm designing an adaptor for a drinks optic and have translated one of the aspects of the design into the following problem. There is plenty of stuff on the net about simple inclined plane problems but not quite like this.
In this problem the blue wedge can only move horizontally, constrained by the fixed green floor. The orange pin (viewed here end on) can only move vertically. It doesn't roll and is constrained by the fixed green wall.
The idea of this mechanism (if you haven't already guessed) is that the pin is raised by pushing the wedge under it.
The pin is pressed down by force Fdown.
The wedge is moved horizontally by Fmove.
Ignore gravity.
I need to determine the angle theta in terms of Fdown, μa & μb at the threshold of moving.
As I say, lots of stuff on the net on inclined planes, friction / frictionless, accelerating / equilibrium, but none quite the same as this where the inclined plane is moving under the pin.
At threshold of moving Fmove = Fdown.
ΣFx = ΣFy = 0
μwall-pin = μpin-wedge = μa.
μwedge-floor = μb.
I've drawn that many FBDs that it's not worth uploading them all. Suffice to say I know about component forces but I just can't figure how to make everything balance.
Thank you please!
1. Homework Statement
I'm designing an adaptor for a drinks optic and have translated one of the aspects of the design into the following problem. There is plenty of stuff on the net about simple inclined plane problems but not quite like this.
In this problem the blue wedge can only move horizontally, constrained by the fixed green floor. The orange pin (viewed here end on) can only move vertically. It doesn't roll and is constrained by the fixed green wall.
The idea of this mechanism (if you haven't already guessed) is that the pin is raised by pushing the wedge under it.
The pin is pressed down by force Fdown.
The wedge is moved horizontally by Fmove.
Ignore gravity.
I need to determine the angle theta in terms of Fdown, μa & μb at the threshold of moving.
As I say, lots of stuff on the net on inclined planes, friction / frictionless, accelerating / equilibrium, but none quite the same as this where the inclined plane is moving under the pin.
Homework Equations
At threshold of moving Fmove = Fdown.
ΣFx = ΣFy = 0
μwall-pin = μpin-wedge = μa.
μwedge-floor = μb.
The Attempt at a Solution
I've drawn that many FBDs that it's not worth uploading them all. Suffice to say I know about component forces but I just can't figure how to make everything balance.
Thank you please!